it depends on the game if they accept images as proof (very few if any do) but you can upload the image to somewhere like imgur and link that
how dare you
"SioN" is short from "Silent Onion" by taking first two letters of the words and "Silent Onion" became a thing when i was playing YGOPRO in 2016 and saw someone with the name "Onion" playing and i just liked it but i didnt want to "copy" his name so i put "Silent" in front of it because im a quiet guy
many people do and there is no reason not to use one if you cant play it on console for somereason also as i live in finland i have pal consoles so early consoles like my n64 cant even compare with the ntsc-u and ntsc-j consoles so the cheapest solution is to emulate of course i could buy an ntsc console which would cost like 50€ to 80€ (guess) and then shipping from where ever and if its outside of eu ill have to pay customs
from what i understood with my tiny brain you want to be in a voice call while streaming but not having the voice call in the stream?
if the quality is good enough and that you can hear the game it doesnt matter if you record with a phone or something but of course you should ask the mods the minimum requirements if you want to be sure
some games accept FCEUX, the accepted emulators should be in the rules of the category but if they are not ask either in the communitys own discord or in the game forums
for a timer you want livesplit
and for any other useful recourses you can find here -> https://www.speedrun.com/resources (livesplit download can be found there)
and you cant really make a submission for a category that doesnt exist but you can always ask the games moderators if they would like to add the category for the game and then if they do add it you can submit your run there
if by "screen" you mean pc/laptop you dont need a capture card you just need to get a recording software but if you meant console gameplay do what Timmiluvs said
ive got the AVerMedia LGX (not sold anymore to my knowledge but the LGX2 is still sold) and it does hdmi and component recording with very low latency (1080p 60fps at max) i bought it for 150€ at the time and ive been really happy with it. my friend bought the LGX2 and he has been happy with that.
also from my friend's experience i wouldnt recommend the elgato, my friend constantly had problems with it. sometimes it just refused to show the video or audio. of course he might have just been unlucky but keep that in mind :P
video editor is what you are looking for